A conical reservoir has a depth of 24 feet and a circular top of radius 12 feet. It is being filled so that the depth of water i increasing at a constant rate of 4 feet per hour. Determine the rate in cubic feet per hour at which water is entering the reservoir when the depth is 5 feet.

I know that A= 1/3(pi)hr^2 but i havent done rates for a while and I don't remember how to do this. Its calc ab

Feb 18th 2009, 05:23 PM

skeeter

...

sub in h/2 for r, and get the volume formula strictly in terms of h ...

now take the time derivative and determine

Feb 19th 2009, 06:19 PM

OnMyWayToBeAMathProffesor

so then . I get that, I would think you would just plug in 5 to get but then where does the 4 feet per hour come in? Thanks for everyones help.

Feb 19th 2009, 06:39 PM

skeeter

Quote:

Originally Posted by OnMyWayToBeAMathProffesor

so then . I get that, I would think you would just plug in 5 to get but then where does the 4 feet per hour come in? Thanks for everyones help.

chain rule ...

Feb 19th 2009, 06:49 PM

OnMyWayToBeAMathProffesor

aaaa, i see. Sorry, I totally forgot about that. But is my formula correct? My peers got different derivative equations. If it is, this would be the subsequent work.